Questions tagged [binomial-distribution]

The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". Use this tag for questions about data that might be binomially distributed or for questions about the theory of this distribution.

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19 views

Transforming the expected value of $Y_i$ in binomial regression

Currently, I'm learning generalized linear regression (GLM). There is something troubling me concerning binomial regression. In this text, in the part about the structure of a GLM, the random ...
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23k views

Logistic Regression: Bernoulli vs. Binomial Response Variables

I want to perform logistic regression with the following binomial response and with $X_1$ and $X_2$ as my predictors. I can present the same data as Bernoulli responses in the following format. The ...
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Understanding Binomial Classifier

In trying to predict the binary class label $y∈\{0,1\}$ given the input $x$, how can I avoid making assumptions about the data, what are the forms of the distributions and how many parameters do I ...
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24 views

How to calculate mean and proportion from a binomial distribution?

Lets say that I flip a coin and get heads 50/200 times. What would my proportion and mean be for this binomial distribution? I am getting confused, because in a binomial distribution there are only 2 ...
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1answer
281 views

binomial pairs probability

A group of four people is said to be “interesting", if there are at most five pairs who are friends. Assume that each pair of people are friends, independent of every other pair, with probability 1/2 ....
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329 views

Are there better estimators of misclassification error than the fraction of misclassified test points?

Assume we train a binary classification model using the training set. Also assume that the model returns an estimate of the probability of success $\hat f(x)$ for every feature vector $x$ and was ...
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Can I use age category as a inflating factor and current age (continuous) as an offset variable in zero inflated negative binomial model?

I am predicting the effect of women empowerment on children ever born using zero inflated negative binomial model. I want to use current age of women as an offset variable. Is it right to use current ...
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2answers
15k views

Confidence interval around binomial estimate of 0 or 1

What is the best technique to calculate a confidence interval of a binomial experiment, if your estimate is that $p=0$ (or similarly $p=1$) and sample size is relatively small, for example $n=25$?
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43 views

Confidence interval of the mean of derived random variables

I have two random variables modeled by a Binomial each: $$X_1 \sim Bin(n_1, p_1)$$ $$Y_1 \sim Bin(n_2, p_2)$$ For each of those random variables I have one observation each. Based on that observation ...
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1answer
35 views

Implicit Ordering in Bernoulli Distributions?

Let $X$ be a Bernoulli random variable with success parameter $p$ As we usually consider the support as $\{0, 1\}$, we write $P(X = 1) = p$ and $P(X = 0) = 1-p$ This $0,1$-encoding seems to induce an ...
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772 views

Appropriate GLM when response variable is proportion, but not binomial

The response variable I'm dealing with is the proportion of a total area that is suitable habitat for a species of interest. So although the response variable is bounded between 0 and 1, my intuition ...
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1answer
242 views

Bayesian inference for Beta distribution after an uncertain outcome

Normally, when we have $$p\sim Beta(a,b)$$ and an observation of $x=1$ (''success'') from a Bernoulli trial with ''success'' probability $p$, the Bayesian inference on the parameter value $p$ is $$p|x\...
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What is wrong with this proof of the variance of a binomial distribution?

Obviously the variance isn’t zero, but I’m missing some foundational understanding and am having a hard time identifying why the setup is wrong: Already answered with comments but this is my question ...
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1answer
181 views

binomial correlation?

I am interested in testing for a correlation between two variables, both of which are binomial. I guess this is equivalent to a Model II regression where both variables are binomial. Ideally I want ...
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1answer
22 views

Understanding/reporting model checks for binomial GLM's - what are the model checks telling me?

I have two binomial GLM's, one of which has passed model checks and the other has not. I have checked the model fits by extracting resids and examined their distributions in histograms. Observations ...
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Is there a simple method to produce a histogram of the Wilson distribution? [closed]

The Wilson score for some observed binomial distribution $(\hat{p},N)$ gives you a confidence interval on $p$. However, I need a histogram over the possible values of $p$. (With a relatively low ...
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Are there small-sample cases where we can approximate the distribution of the Wald statistic better than with the Normal/Chi-squared distribution?

In my specific case, I'm referring to the parameter estimates of a binomial regression (regardless of whether we are estimating risk ratios or odds ratios). Can the problem of divergence of the Wald ...
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Can an inference be made about how an outcome might look with “more power”?

I have a binomial outcome that I have compared across two groups: Control - 21/783 occurrences (2.68%, 1.71-4.14% 95% CI) Experimental - 13/261 occurrences (4.98%, 2.79-8.57%, 95% CI) The p value is ...
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2answers
114 views

A method for simplifying manual random number generation? [closed]

Is there a good way to take a more complicated dice-rolling mechanism and create a simpler dice-rolling mechanism that gives roughly similar results? Example 1: Say you have a game where both sides ...
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Binomial distribution for gender discrimination?

I could be on the wrong path, but I'm trying to use binomial distribution to identify gender discrimination and am having issues getting consistent results based on trial size(?)... I think. Small ...
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1answer
26 views

How compare relative frequencies between different sized groups (fish species)?

I have gathered data from a number of studies on presence / absence of fish species at 4 locations (let's call them A-D) with different proximity to a structure. I am interested in knowing how ...
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1answer
30 views

Can I use construct/factor (revealed by EFA) mean scores as explanatory variables in a GLM (binomial family)?

I have 11 motivations (M1-M11) in my questionnaire for ocean swimming. After running an EFA, I detected 4 underlying latent factors (relaxation, socialization, etc.) which explained about 58% of the ...
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Understanding correlation between estimated class probabilities for multinomial distribution

Suppose that I estimate class probabilities for a multinomial distribution with three classes using individual binomial confidence intervals. I'd like to create a confidence interval the error around ...
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31 views

How handle frequency data to make it comparable between different sized samples?

I have gathered data on presence / absence of objects at 4 different locations from a number of studies (12 to be exact). I am interested in knowing how frequently each of these objects are recorded ...
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21 views

how to compare variances of two binomial traits that have very different means?

I want to estimate and compare the among-line variance of two binomial traits (A and B) that have different mean values (0.67 and 0.92, respectively). For this, I have been using the lme4 (v. 1.1-27.1)...
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355 views

Test of Signficiance for Win Percentage

I am looking at the win percentage of a teams using 3 defenders versus teams using 4 defenders and would like to see if the difference in means is statistically signifcant and test within R. However, ...
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100 views

Doubt if hypothesis test is correct (one vs. two tail)

I am trying to do a hypothesis test but I do not know if I am doing the correct steps for this. I started to define the hypothesis for a binomial proportion $p$ as: H0: A test suite cannot detect ...
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2answers
260 views

mle for the binomial distributed data

For example i have following dataset of number of boys in families that have 5 kids: 0 boy - 34 (number of such families) 1 boy - 128 families 2 boys - 233 families 3 boys - 267 families 4 boys - 144 ...
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Binomial riddle [closed]

I have a riddle that i cannot solve: I'm a recruiter searching for the best basketball player in a town. There are 100 candidates in the town. 99 of them have a probability of basket the ball of 0.501,...
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1answer
174 views

What is the proper way to estimate the probability (proportion of time) a rare event occurs?

Often, I need to estimate the probability (proportion of time) a rare event occurs. The standard MLE estimate often gives me extreme estimates since the denominator is usually 1, and the numerator is ...
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49 views

Do I need to find sum each PDF individually to find the CDF

The probability is 0.316 that an audit of a retail business will turn up irregularities in the collection of state sales tax. If 16 retail businesses are audited, find the probability that: (b) at ...
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How many orders will be placed on average until stock runs out, given a probability that the customer will find the item they want?

Let there be 500 units of stock $s$ of diverse items in a store. Customers arrive one by one and, for every given item, there is a likelihood $m$ of 5% that it is precisely the item that the customer ...
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1answer
31 views

Approximate binomial dist in sql

What is the best way of approximating a binomial distribution, given I have the following functions available: normal_cdf ...
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22 views

Prediction plot from binomial glm/regression - prediction line does not go up to 1 on the y-axis

I have a binomial glm looking at the probability of an otter road traffic accident occurring when considering a host of environmental factors. Model is running fine, but the prediction plot line for ...
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59 views

Finding an unbiased estimate for $p$, binomial distribution

An experiment is conducted to study the effect of a power surge on data stored in a digital computer. A "word" is a sequence of 8 bits. each bit is either "on" (activated) or "...
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Binomial Proportion Test on test and control populations [duplicate]

I am new to statistical tests and request your help with the following question: A company wants to test the hypothesis that it's new ad will increase it's total number of subscribers (conversion rate)...
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2answers
186 views

Binomial logistic regression for multiclass problems

Applying the independence of irrelevant alternatives (IIA) is an inherent assumption in multinomial logistic regression but not binomial. Is it therefore okay and possibly better to use $K$ binomial ...
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1answer
60 views

Binomial vs. proportional odds logistic regression

I have some clinical data, blood lab values (continuous) and clinical scores (ordinal: 0, 1, ..., 5), and I'd like to model the score as a function of the blood values. I know I could perform ...
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1answer
53 views

Bounds over expected value of reciprocal binomial random variable

Given a binomial random varible $N \sim \text{Bin}(n,p)$, I want to find an upper bound for the value: $$\phi \equiv \sup_{n \cdot p \geq 1} \mathbb{E} \bigg( \frac{np}{\max(N,1)} \bigg).$$ (Note ...
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13 views

Can I use ROC/AUC to compare binomial GLMM models?

Is there any reason not to use ROC for evaluating the effectiveness of a binomial GLMM model with logit link? In my specific case, I have six models (one null model with two random effects, five other ...
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14 views

Binomial Zero Probability Test

Let's assume a histogram of $K$ cells and $N$ samples. In some bins, the counts are zero, $k(i)$ $i \in [1,K]$. How can I test the probability is really zero (Bayesian) or alternatively what is the p-...
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1answer
497 views

Likelihood function for binomial distribution with label 1 and -1

I am quite curious how we should write the likelihood function for -1, 1 in binomial case? The reason I am asking is because this, one of famous papers on gradient boosting. Just on the first page, he ...
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1answer
47 views

Can statistics be used to answer the following question?

Suppose I am an inactive person - I go for a walk on average a few times a .month (e.g. every day there is a 5% chance I go for a walk, independent of yesterday) . However, each time I go for a walk, ...
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30 views

How to test for significance for binomial count data where the expected outcome is unknown?

Description of the data: The study is investigating whether conversations on a messaging app are greater or less than 8 words long. The variable is the count of messages that contain more than 8 words ...
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1answer
41 views

How do I choose which confident interval for proportion difference to use in SAS?

In SAS, there are different CIs for proportion difference ($\pi_1-\pi_2$) to choose? 1.Continuity-corrected Wald CIs based on normal approximation 2.exact method 3.Miettinen-Nurminen CIs based on ...
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42 views

classical m balls and n bins problem but more tricky

This is a problem related with the classical $n$ bins and $m$ balls problem but has some modifications that makes it more tricky to solve: In this case, the probabilities of the bin´s system are not ...
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Using the bootstrap for estimating the odds ratio standard error

I have the following table $$ \begin{matrix} &R = 0 & R = 1 \\ E = 0 &n_{00} &n_{01}\\ E = 1 &n_{10} &n_{11} \end{matrix} $$ If needed, this is census data from a metropolitan ...
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Evaluating Block Bootstrap Confidence Interval

I have an estimation that is obtained by using MCMC. In order to calculate the standard error of the estimation, I use Block Bootstrap approach and using this standard error I create a 95% confidence ...
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27 views

Model/variable selection in binomial models for marble counts?

Thank you in advance for your help with this interesting question that has come up in my research. I changed the problem to bags/marbles to simplify. Problem description There are N bags, each ...
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27 views

Interpretation of logistic regression - interaction between predictors

Context: Workbook question for my high-school statistics subject An experiment was conducted where 30 parasitic worms of each sex were poisoned at each of five dosages, and the number of deaths were ...

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